Chandra observations of distant elliptical galaxies have
revealed large numbers of Low Mass X-ray Binaries (LMXBs)
accreting near the Eddington limit. The majority of these
LMXBs reside in globular clusters (GCs) and it has been
suggested that many of the field LMXBs also originated in
GCs. We show here that ultracompact binaries with orbital
periods of 8-10 minutes and He or C/O donors of 0.06-0.08
solar masses naturally provide the observed accretion rates
from gravitational radiation losses alone. Such systems are
predicted to be formed in the dense GC environment, a
hypothesis supported by the 11.4 minute binary 4U 1820-30,
the brightest persistent LMXB in a Galactic GC. These
binaries have short enough lifetimes (less than 3 Myrs)
while bright that we calculate their luminosity function
under a steady-state approximation. This yields a luminosity
function slope in remarkable agreement with that observed.
This agreement encourages us to use the observed numbers of
LMXBs per GC mass to calculate the accumulated number of
ultracompact binaries. For a constant birthrate over 8 Gyrs,
the number of ultracompact binaries which have evolved
through this bright phase is 4000 in a 10 million solar mass
GC, consistent with the dynamical interaction calculations
to date. Perhaps most importantly, if all ultracompacts
become millisecond radio pulsars, then the observed
normalization agrees with the inferred number of millisecond
radio pulsars in 47 Tuc.